Einstein warped G2 and Spin(7) manifolds

TL;DR

This paper constructs and characterizes various classes of Einstein G2 and Spin(7) manifolds using warped structures with Einstein SU(3) and G2 fibers, providing explicit torsion form descriptions.

Contribution

It explicitly describes torsion forms of warped G2 and Spin(7) structures and characterizes Einstein warped manifolds with these structures, extending previous classifications.

Findings

Realization of most classes of Einstein G2-structures with various scalar curvatures.

Explicit formulas for torsion forms in terms of torsion of fiber structures.

Characterizations of principal classes of Einstein warped G2 and Spin(7) manifolds.

Abstract

In this paper most of the classes of G2-structures with Einstein induced metric of negative, null or positive scalar curvature are realized. This is carried out by means of warped G2-structures with fiber an Einstein SU(3) manifold. The torsion forms of any warped G2-structure are explicitly described in terms of the torsion forms of the SU(3)-structure and the warping function, which allows to give characterizations of the principal classes of Einstein warped G2 manifolds. Similar results are obtained for Einstein warped Spin(7) manifolds with fiber a G2 manifold.